A284205 Ninth column of Euler's difference table in A068106.

0, 0, 0, 0, 0, 0, 0, 40320, 322560, 2943360, 30078720, 339696000, 4196666880, 56255149440, 812752093440, 12585067447680, 207863095910400, 3646938237505920, 67723519234210560, 1326863186062565760, 27349945952061841920, 591598086412112035200

Offset: 1

Author

Enrique Navarrete, Mar 22 2017

Keywords

• nonn

Comments

For n >= 9, this is the number of permutations of [n] that avoid substrings j(j+8), 1 <= j <= n-8.

Examples

			a(12)=339696000 since this is the number of permutations in S12 that avoid substrings {19,2(10),3(11),4(12)}.
		

Links

• Enrique Navarrete, Generalized K-Shift Forbidden Substrings in Permutations, arXiv:1610.06217 [math.CO], 2016.

Crossrefs

Also 40320 times A176734.

Cf. A068106.

Programs

Mathematica

With[{k = 9}, ConstantArray[0, k - 2]~Join~Table[Sum[(-1)^j*Binomial[n - (k - 1), j] (n - j)!, {j, 0, n - (k - 1)}], {n, k - 1, k + 12}]] (* Michael De Vlieger, Mar 26 2017 *)

Formula

For n>=9: a(n) = Sum_{j=0..n-8} (-1)^j*binomial(n-8,j)*(n-j)!.

Note a(n)/n! ~ 1/e.